Reconstruction of Channelized Facies Using Sparsity Constraints

A new approach is presented for inverse modeling to reconstruct continuous features in space, such as channels, that exhibit sparseness in a complementary basis (e.g. a Fourier basis) using observations in spatial domain. Continuity in space is used to constrain the solution to be sparse in the discrete cosine transform (DCT) domain. The DCT is used to effectively reduce the dimension of the search space to a low frequency subspace to improve estimation efficiency. The methodology is related to compressive sensing, which is a recently introduced paradigm for perfect reconstruction of sparse signals from partial linear measurements in a complementary basis. The suitability of the inversion method is demonstrated through synthetic experiments in characterization of geological facies distribution using scattered point measurements and noise-corrupted areal observations resembling seismic data.